Normal Reflection Research Articles

Transfer of absolute continuity by a flow generated by a stochastic equation with reflection

Let ϕt(x), x ∈ ℝ+ be a value taken at time t ≥ 0 by a solution of a stochastic equation with normal reflection from a hyperplane starting at initial time from x. We characterize the absolutely continuous (with respect to Lebesgue measure) component and the singular component of a stochastic measure-valued process µt = µ ○ ϕt−1 that is the image of a certain absolutely continuous measure µ under random mapping ϕt(·). We prove that the restriction of the Hausdorff measure Hd−1 to the support of the singular component is σ-finite and give sufficient conditions guaranteeing that the singular component is absolutely continuous with respect to Hd−1.

Photometric properties of Titan's surface from Cassini VIMS: Relevance to titan's hemispherical albedo dichotomy and surface stability

The Visual and Infrared Mapping Spectrometer (VIMS) instrument on the Cassini Saturn Orbiter returned spectral imaging data as the spacecraft undertook six close encounters with Titan beginning 7 July, 2004. Three of these flybys each produced overlapping coverage of two distinct regions of Titan's surface. Twenty-four points were selected on approximately opposite hemispheres to serve as photometric controls. Six points were selected in each of four reflectance classes. On one hemisphere each control point was observed at three distinct phase angles. From the derived phase coefficients, preliminary normal reflectances were derived for each reflectance class. The normal reflectance of Titan's surface units at 2.0178 μm ranged from 0.079 to 0.185 for the most absorbing to the most reflective units assuming no contribution from absorbing haze. When a modest haze contribution of τ =0.1 is considered these numbers increase to 0.089–0.215. We find that the lowest three reflectance classes have comparable normal reflectance on either hemisphere. However, for the highest brightness class the normal reflectance is higher on the hemisphere encompassing longitude 14–65° compared to the same high brightness class for the hemisphere encompassing 122–156° longitude. We conclude that an albedo dichotomy observed in continental sized units on Titan is due not only to one unit having more areal coverage of reflective material than the other but the material on the brighter unit is intrinsically more reflective than the most reflective material on the other unit. This suggests that surface renewal processes are more widespread on Titan's more reflective units than on its less reflective units. We note that one of our photometric control points has increased in reflectance by 12% relative to the surrounding terrain from July of 2004 to April and May of 2005. Possible causes of this effect include atmospheric processes such as ground fog or orographic clouds; the suggestion of active volcanism cannot be ruled out. Several interesting circular features which resembled impact craters were identified on Titan's surface at the time of the initial Titan flyby in July of 2004. We traced photometric profiles through two of these candidate craters and attempted to fit these profiles to the photometric properties expected from model depressions. We find that the best-fit attempt to model these features as craters requires that they be unrealistically deep, approximately 70 km deep. We conclude that despite their appearance, these circular features are not craters, however, the possibility that they are palimpsests cannot be ruled out. We used two methods to test for the presence of vast expanses of liquids on Titan's surface that had been suggested to resemble oceans. Specular reflection of sunlight would be indicative of widespread liquids on the surface; we found no evidence of this. A large liquid body should also show uniformity in photometric profile; we found the profiles to be highly variable. The lack of specular reflection and the high photometric variability in the profiles across candidate oceans is inconsistent with the presence of vast expanses of flat-lying liquids on Titan's surface. While liquid accumulation may be present as small, sub-pixel-sized bodies, or in areas of the surface which still remain to be observed by VIMS, the presence of large ocean-sized accumulations of liquids can be ruled out. The Cassini orbital tour offers the opportunity for VIMS to image the same parts of Titan's surface repeatedly at many different illumination and observation geometries. This creates the possibility of understanding the properties of Titan's atmosphere and haze by iteratively adapting models to create a best fit to the surface reflectance properties.

On maximal inequalities for some jump processes

We present a solution to the considered in [5] and [22] optimal stopping problem for some jump processes. The method of proof is based on reducing the initial problem to an integro-differential free-boundary problem where the normal reflection and smooth fit may break down and the latter then be replaced by the continuous fit. The derived result is applied for determining the best constants in maximal inequalities for a compound Poisson process with linear drift and exponential jumps.

Titan: Preliminary results on surface properties and photometry from VIMS observations of the early flybys

Cassini observations of the surface of Titan offer unprecedented views of its surface through atmospheric windows in the 1–5 μm region. Images obtained in windows for which the haze opacity is low can be used to derive quantitative photometric parameters such as albedo and albedo distribution, and physical properties such as roughness and particle characteristics. Images from the early Titan flybys, particularly T0, Ta, and T5 have been analyzed to create albedo maps in the 2.01 and 2.73 μm windows. We find the average normal reflectance at these two wavelengths to be 0.15±0.02 and 0.035±0.003, respectively. Titan's surface is bifurcated into two albedo regimes, particularly at 2.01 μm. Analysis of these two regimes to understand the physical character of the surface was accomplished with a macroscopic roughness model. We find that the two types of surface have substantially different roughness, with the low-albedo surface exhibiting mean slope angles of ∼18°, and the high-albedo terrain having a much more substantial roughness with a mean slope angle of ∼34°. A single-scattering phase function approximated by a one-term Henyey–Greenstein equation was also fit to each unit. Titan's surface is back-scattering ( g∼0.3–0.4), and does not exhibit substantially different backscattering behavior between the two terrains. Our results suggest that two distinct geophysical domains exist on Titan: a bright region cut by deep drainage channels and a relatively smooth surface. The two terrains are covered by a film or a coating of particles perhaps precipitated from the satellite's haze layer and transported by eolian processes. Our results are preliminary: more accurate values for the surface albedo and physical parameters will be derived as more data is gathered by the Cassini spacecraft and as a more complete radiative transfer model is developed from both Cassini orbiter and Huygens Lander measurements.

Calculation of the optical and electronic properties of TiN x thin films on domain IR–VIS–UV

In this paper, the dependence of the optical properties of thin titanium nitride films deposited by reactive DC magnetron sputtering on different nitrogen pressures, as well as the electrical properties and mechanical properties is investigated. The normal reflectivity is measured in a range from 0.5 to 5.5 eV. The results have been fitted using a dielectric function which takes into account the presence of several Lorentz oscillators. Contributions to the absorption due to bound and conduction electrons are separated. This approach allows the computation of the mean free path of conduction electrons, screened plasma energy, and the optical conductivity, which informed about the nature of the defects in TiN x compound.

Local and nonlocal entanglement for quasiparticle pairs induced by Andreev reflection

We investigate local and nonlocal entanglement of particle pairs induced by direct and crossed Andreev reflections at the interfaces between a superconductor and two normal conductors. It is shown theoretically that both local and nonlocal entanglement can be quantified by concurrence and detected from the violation of a Bell inequality of spin current correlators, which are determined only by normal reflection and Andreev reflection eigenvalues. There exists a one-to-one correspondence between the concurrence and the maximal Bell-CHSH parameter in the tunneling limit.

Crack‐free AlGaN/GaN Bragg mirrors grown on Si (111) substrates by metalorganic vapor phase epitaxy

AbstractCrack‐free distributed Bragg reflectors (DBR) with high reflectance and high Al content were grown over Si (111) substrates by metalorganic vapor phase epitaxy. This is achieved by introducing a set of nine period AlN / GaN short‐period superlattices (SL) with average Al content of 50% instead of the bulk Al0.5Ga0.5N. We found that the AlN / GaN superlattices not only decreased the tensile strain but also improved the reflectance. Moreover, this structure also improves the surface roughness and reduces the dislocation densities. The larger refractive index ratio between high‐Al‐content AlxGa1‐xN and GaN permits one to obtain a spectral stopband width of 25 nm and a reflectance value 62% at 480 nm for 7 mirror periods. We present the experimental and simulation results and the characterization by normal direction reflectance spectrum, high resolution x‐ray diffraction (HRXRD), field emission scanning electron microscopy (SEM) and atomic force microscopy (AFM). (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A linear approximation for the regular reflection of a weak shock at a wedge satisfying sonic condition

The problem of shock reflection by a wedge, which the flow is dominated by the unsteady potential flow equation, is a important problem. In weak regular reflection, the flow behind the reflected shock is immediately supersonic and becomes subsonic further downstream. The reflected shock is transonic. Its position is a free boundary for the unsteady potential equation, which is degenerate at the sonic line in self-similar coordinates. Applying the special partial hodograph transformation used in [Zhouping Xin, Huicheng Yin, Transonic shock in a nozzle I, 2-D case, Comm. Pure Appl. Math. 57 (2004) 1–51; Zhouping Xin, Huicheng Yin, Transonic shock in a nozzle II, 3-D case, IMS, preprint (2003)], we derive a nonlinear degenerate elliptic equation with nonlinear boundary conditions in a piecewise smooth domain. When the angle, which between incident shock and wedge, is small, we can see that weak regular reflection as the disturbance of normal reflection as in [Shuxing Chen, Linear approximation of shock reflection at a wedge with large angle, Comm. Partial Differential Equations 21 (78) (1996) 1103–1118]. By linearizing the resulted nonlinear equation and boundary conditions with above viewpoint, we obtain a linear degenerate elliptic equation with mixed boundary conditions and a linear degenerate elliptic equation with oblique boundary conditions in a curved quadrilateral domain. By means of elliptic regularization techniques, delicate a priori estimate and compact arguments, we show that the solution of linearized problem with oblique boundary conditions is smooth in the interior and Lipschitz continuous up to the degenerate boundary.

Aromatic Polyesters with Flexible Side Chains. 10. Studies on Biaxiality in Nematic Liquid Crystal of BC-n Polyester

This paper reports a possibility of biaxiality in the nematic liquid crystal formed from aromatic polyesters, BC-n, which are composed of 1,4-dialkyl ester of pyromellitic acid and 4,4′-biphenol. In these BC-n polyesters, as a general trend, the microsegregation of aromatic backbone and flexible side chains takes place and the nematic liquid crystal appears after these layered phases melt. X-Ray diffraction pattern from oriented nematic fiber shows unusual inner reflection with a large spacing around 20 A in addition to normal outer reflection with a spacing of 4.5 A on equatorial line, indicating that there are two types of packing correlation in a direction perpendicular to the director, n, in other words, there is a biaxiality. Optical microscopic textures exhibit exclusively the two-brush disclinations with |s|=1/2, which also conforms to the biaxial nematic order. The spacing of inner equatorial reflection approximates to the layer spacing in the layered mesophase formed from the same homologues. This strongly suggests that the layered aggregation is still remained in the nematic liquid crystals, and its board-like shape is responsible for the biaxiality.

Acoustic Emission in Wide Composite Specimens

Acoustic emission (AE) is an attractive technique for the structural health monitoring (SHM) of aerospace systems. To reach its full potential in this role a quantitative approach must be adopted to study damage mechanisms in composite materials. In this paper, some of the practical issues regarding acoustic emission testing in composites are addressed. A model describing Lamb wave propagation through plates is described and used to make phase velocity and attenuation measurements in both aluminium and carbon fibre reinforced plastic plates. Results are then implemented in the frequency domain to conduct an experimental study of normal incidence Lamb wave reflections. Comparisons are made with finite element analysis (FEA) models with good results.

In situ determination and control of AlGaInP composition during MOVPE growth

The influence of composition changes in (Al x Ga 1− x ) 1− y In y P grown on GaAs in metal-organic vapour-phase epitaxy on the in situ measured optical signals reflectance anisotropy (RA) and normalized reflectance (NR) is studied. The aluminium composition x (band gap) is changed from 0 to 1 while the indium composition y (lattice matching) is adjusted about ±0.03 around the lattice matched value of y=0.48. The optical signals were correlated to the composition which was determined by ex situ measurements. A strong influence of both compositions x and y, respectively, is observed in the RA and the NR spectra and transients. The composition changes have an influence on the amplitude as well as on the energetic positions of the respective features in the RA spectra. A strong influence of the composition on the first amplitude of the UV Fabry–Perot interference in the time-resolved NR signal can be seen. Very thin layers, 12 nm, are sufficient for the in situ determination of the composition. The results are used for in situ composition calibration procedures.

Seismic Data Processing and the Characterization of a Gas Hydrate Bearing Zone Offshore of Southwestern Taiwan

Various seismic attributes of gas hydrate bearing sediments were analyzed in the accretionary prism offshore of southwestern Taiwan utilizing seismic imaging, velocity analysis, AVO analysis, and AVO inversion of large offset seismic data. A bottom-simulating reflector (BSR) is clearly observed on the seismic section with a reversed polarity compared to that of the seabed reflection. Instantaneous amplitude sectioning clearly shows lateral variations of the BSR. The zero-phase waveform of the BSR is distinct and the weak reflectors above the BSR can be observed on the instantaneous phase section. AVO analysis shows the absolute value of the negative BSR amplitude increasing with offset. A low P-wave interval velocity layer was found below the strong BSR by detailed velocity analysis. Both the P (normal incident P-wave reflection coefficient) and G (AVO gradient) values are highly negative for the strong BSR on the P and G sections, and they lie in the third quadrant of the P and G cross-plot section. The P+G (reflectivity of Poisson's ratio) value is also negative on the P+G section and the P-G (normal incident S-wave reflection coefficient) value is approximately zero on the P-G section along the same strong BSR. All the seismic characters described above suggest that a gas hydrate layer exists together with a free gas layer below it along strong BSRs in the area offshore southwestern Taiwan.

Optical Coherence Tomography in Progressive Outer Retinal Necrosis

<P>A 38-year-old man with human immunodeficiency virus was referred for evaluation of retinal lesions in both eyes. Optical coherence tomography was performed after dilating the pupils. Biomicroscopy of the retina showed an atypical, solitary, yellowish-white lesion in the macula of both eyes with no inflammation of the vitreous. Optical coherence tomography of the lesions showed an area of extremely low reflectivity with well-defined but irregular borders in the outer retina. The surrounding retina showed normal reflectivity and was of normal thickness. Optical coherence tomography showed selective necrosis of the outer layers due to progressive outer retinal necrosis. Optical coherence tomography may serve as a useful tool for the early diagnosis of progressive outer retinal necrosis. [<CITE>Ophthalmic Surg Lasers Imaging</CITE> 2006;37:506-507.] </P> <H4>AUTHORS</H4> <P>From the Department of Ophthalmology (RN, BDK), University of California, Irvine, California; and the L. V. Prasad Eye Institute (RN), Hyderabad, India. </P> <P>Accepted for publication August 4, 2006. </P> <P>Presented at the annual meeting of the Association for Research in Vision and Ophthalmology, May 1-5, 2005, Fort Lauderdale, Florida. </P> <P>Address reprint requests to Baruch D. Kuppermann, MD, PhD, Department of Ophthalmology, University of California–Irvine, 118 Med Surge I, Irvine, CA 92697-4375.</P>

Application of the homogenization approximation to rough one-dimensional photonic crystals

As previously reported [Opt. Lett. 29, 2791 (2004)], one-dimensional photonic crystals exhibit a decrease in their normal reflectivity if their interfaces are not flat. We show that the homogenization approximation accurately predicts this diminished optical response by comparing results with finite-difference time-domain (FDTD) simulations applied to the same roughened structures. Within the parameter range tested (rms roughness < 20% and rms wavelengths < 100% of the photonic crystal periodicity), the homogenization approximation accurately reproduces the reflectivities obtained by the FDTD simulations, which are much more computationally expensive.

A linear approximation for the regular reflection of a weak shock at a wedge

The problem of shock reflection by a wedge in the flow dominated by the unsteady potential flow equation is an important problem. In weak regular reflection, the flow behind the reflected shock is immediately supersonic and becomes subsonic further downstream. The reflected shock is transonic. Its position is a free boundary for the unsteady potential equation, which is degenerate at the sonic line in self-similar coordinates. Applying the special partial hodograph transformation used in [Zhouping Xin, Huicheng Yin, Transonic shock in a nozzle I, 2-D case, Comm. Pure Appl. Math. LVII (2004) 1-51; Zhouping Xin, Huicheng Yin, Transonic shock in a nozzle II, 3-D case, IMS, preprint, 2003], we derive a nonlinear degenerate elliptic equation with nonlinear boundary conditions in a piecewise smooth domain. When the angle between incident shock and wedge is small, we can see the weak regular reflection as the disturbance of normal reflection as in [Chen Shuxing, Linear approximation of shock reflection at a wedge with large angle, Comm. Partial Differential Equations 21(78) (1996) 1103–1118]. By linearizing the resulted nonlinear equation and boundary conditions with the above viewpoint in [Chen Shuxing, Linear approximation of shock reflection at a wedge with large angle, Comm. Partial Differential Equations 21(78) (1996) 1103–1118], we obtain a linear degenerate elliptic equation with mixed boundary conditions in a curved quadrilateral domain. By means of elliptic regularization techniques, a delicate a priori estimate and compact arguments, we show that the solution of the linearized problem is smooth in the interior and Lipschitz continuous up to the degenerate boundary.

Optical Determination of Differential Coverage−Potential Relations of Redox-Active Species Immobilized on Electrode Surfaces

Single-wavelength (HeNe laser, lambda = 633 nm), normal incidence UV-visible reflectance spectroscopy was used to monitor the optical properties of the glassy carbon (GC)|0.2 M NaOH(aq) interface as a function of the applied potential, E. Whereas the electroreflectance coefficient for bare GC was found to be small and potential independent, surface functionalization by an irreversibly adsorbed layer of tetrasulfonated cobalt phthalocyanine (CoTSPc) yielded a clearly defined sigmoidally shaped normalized reflectance change (DeltaR/R) vs E curve over the potential region in which the adsorbate displayed redox peaks. Assuming DeltaR/R is proportional to the extent of redox conversion, as has been reported for macrocycles adsorbed on other types of carbon (e.g., Kim, S.; Xu, X.; Bae, I. T.; Wang, Z.; Scherson, D. A. Anal. Chem. 1990, 62, 2647-2650), differential coverage-potential relations were determined based purely on the optical data collected. A similar optical behavior was found for irreversible adsorbed CoPc and tetraamino CoPc (CoTAPc) adsorbed on GC, for which the voltammetric peaks were ill-defined, too small for coulometric analyses to be reliably performed, or both. No detectable changes in the DeltaR/R vs E profiles of either bare or macrocyclic-functionalized surfaces were observed upon addition of hydrazine to the neat 0.2 M NaOH solution at potentials at which these surfaces display electrocatalytic properties for its oxidation. Possible factors responsible for this behavior are discussed.

Development and control of MOVPE growth processes for devices using reflectance anisotropy spectroscopy and normalized reflectance

AbstractThe use of the optical in situ techniques reflectance anisotropy (RA) and normalized reflectance (NR) for metal‐organic vapour‐phase epitaxy (MOVPE) growth processes of compound semiconductor devices is reviewed. The RA signal detects small deviations in the doping profile during growth of hetero‐bipolar transistors and correlates to the emission wavelength of edge‐emitting laser structure via its sensitivity to the quantum well composition. The NR signal is crucial for the alignment of distributed Bragg reflectors (DBR) in vertical‐cavity surface‐emitting lasers. With simultaneously performed RA and NR measurements the doping profile as well as the DBR alignment can be determined in situ. The composition monitoring in quaternary InGaAsP grown on InP is demonstrated using the RA signal for the As:P ratio while the NR signal is used for the Ga:In ratio. For AlGaInP on GaAs the NR signal is sensitive to both the aluminium and the indium content. Therefore these effects have to be separated via the determination of the growth efficiency of the respective materials using the growth rate calculated from the NR signal. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Nonlocal pure spin current injection via quantum pumping and crossed Andreev reflection

A pure spin current injector is proposed based on adiabatic pumping and crossed normal and Andreev reflection. The device consists of a three-terminal ferromagnet-superconductor-semiconductor system in which the injection of a pure spin current is into the semiconductor which is coupled to the superconductor within a coherence length away from the ferromagnet enabling the phenomena of crossed normal/Andreev reflection to operate. Quantum pumping is induced by adiabatically modulating two independent parameters of the ferromagnetic lead, namely, the magnetization strength and the strength of coupling between the ferromagnet and the superconductor. The competition between the normal/Andreev reflection and the crossed normal/Andreev reflection, both induced by pumping, leads to nonlocal injection of a pure spin current into the semiconductor. The experimental realization of the proposed device is also discussed.

Properties of the Flows Generated by Stochastic Equations with Reflection

We consider the properties of a random set ϕ t (ℝ + d ), where ϕ t (x) is a solution of a stochastic differential equation in ℝ + d with normal reflection from the boundary that starts from a point x. We characterize inner and boundary points of the set ϕ t (ℝ + d ) and prove that the Hausdorff dimension of the boundary ∂ϕ t (ℝ + d ) does not exceed d − 1.

Clean and dirty superconductivity in pure, Al-doped, and neutron irradiatedMgB2: A far-infrared study

The effects of Al substitution and neutron irradiation on the conduction regime (clean or dirty) of the $\pi$- and $\sigma$-band of MgB$_{2}$ have been investigated by means of far-infrared spectroscopy. The intensity reflected by well characterized polycrystalline samples was measured up to 100 cm$^{- 1}$ in both normal and superconducting state. The analysis of the superconducting to normal reflectivity ratios shows that only the effect of the opening of the small gap in the dirty $\pi$-band can be clearly observed in pure MgB$_{2}$, consistently with previous results. In Al-doped samples the dirty character of the $\pi$-band is increased, while no definitive conclusion on the conduction regime of the $\sigma $-band can be drawn. On the contrary, results obtained for the irradiated sample show that the irradiation-induced disorder drives the $\sigma$-band in the dirty regime, making the large gap in $\sigma$-band observable for the first time in far-infrared measurements.